1. Uniform

Ketinggian bibit sayur organic

set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010

n <- 400
data_bibit <- runif(n, min = 15, max = 45) # cm

Tentukan:
1) Densitas pada x = 28
2) CDF pada q = 28
3) Kuantil pada p = 0.25
4) Probabilitas antara 20 dan 35 cm
5) Statistik deskriptif (mean, median, sd, skewness, kurtosis)
6) Plot density & histogram (overlay theoretical uniform pdf)
7) Uji kesesuaian ke distribusi uniform (mis. KS test atau chi-square binned)

set.seed(013)
n <- 400
data_bibit <- runif(n, min = 15, max = 45)

# 1) Densitas pada x = 28
x <- 28
densitas <- dunif(x, min = 15, max = 45)
densitas
## [1] 0.03333333
# 2) CDF pada q = 28
cdf <- punif(q = 28, min = 15, max = 45)
cdf
## [1] 0.4333333
# 3) Kuantil pada p = 0.25
kuantil <- qunif(p = 0.25, min = 15, max = 45)
kuantil
## [1] 22.5
# 4) Probabilitas antara 20 dan 35 cm
prob <- punif(35, 15, 45) - punif(20, 15, 45)
prob
## [1] 0.5
# 5) Statistik deskriptif
library(moments)
mean_val <- mean(data_bibit)
median_val <- median(data_bibit)
sd_val <- sd(data_bibit)
skew_val <- skewness(data_bibit)
kurt_val <- kurtosis(data_bibit)

stat_deskriptif <- data.frame(
  Mean = mean_val,
  Median = median_val,
  SD = sd_val,
  Skewness = skew_val,
  Kurtosis = kurt_val
)
stat_deskriptif
# 6) Plot density & histogram (overlay dengan PDF uniform teoretis)
hist(data_bibit, breaks = 20, freq = FALSE, col = "skyblue",
     main = "Histogram dan PDF Teoretis Uniform(15,45)",
     xlab = "Panjang Bibit (cm)")
curve(dunif(x, 15, 45), add = TRUE, col = "red", lwd = 2)

# 7) Uji kesesuaian distribusi uniform
# a) Uji Kolmogorov–Smirnov
ks_test <- ks.test(data_bibit, "punif", min = 15, max = 45)
ks_test
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  data_bibit
## D = 0.048897, p-value = 0.2944
## alternative hypothesis: two-sided
# b) Uji Chi-square binned
observed <- hist(data_bibit, breaks = seq(15, 45, by = 3), plot = FALSE)$counts
expected <- rep(n / length(observed), length(observed))
chisq_test <- chisq.test(observed, p = rep(1 / length(observed), length(observed)))
chisq_test
## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 17.8, df = 9, p-value = 0.03757

2. Exponential

Waktu respon server (detik)
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010

n <- 600
rate <- 1/2 # rata-rata 2 detik
data_respon <- rexp(n, rate = rate)

Tentukan:
1) Densitas pada x = 1.5
2) CDF pada q = 1.5
3) Kuantil pada p = 0.8
4) Probabilitas antara 0.5 dan 3 detik
5) Statistik deskriptif
6) Plot density & histogram (bandingkan histogram dengan teoritis)
7) Uji kesesuaian distribusi eksponensial

set.seed(013)
n <- 600
rate <- 1/2   # rata-rata = 2 detik
data_respon <- rexp(n, rate = rate)

# 1) Densitas pada x = 1.5
x <- 1.5
densitas <- dexp(x, rate = rate)
densitas
## [1] 0.2361833
# 2) CDF pada q = 1.5
cdf <- pexp(q = 1.5, rate = rate)
cdf
## [1] 0.5276334
# 3) Kuantil pada p = 0.8
kuantil <- qexp(p = 0.8, rate = rate)
kuantil
## [1] 3.218876
# 4) Probabilitas antara 0.5 dan 3 detik
prob <- pexp(3, rate = rate) - pexp(0.5, rate = rate)
prob
## [1] 0.5556706
# 5) Statistik deskriptif
library(moments)
mean_val <- mean(data_respon)
median_val <- median(data_respon)
sd_val <- sd(data_respon)
skew_val <- skewness(data_respon)
kurt_val <- kurtosis(data_respon)

stat_deskriptif <- data.frame(
  Mean = mean_val,
  Median = median_val,
  SD = sd_val,
  Skewness = skew_val,
  Kurtosis = kurt_val
)
stat_deskriptif
# 6) Plot density & histogram (overlay dengan PDF teoretis)
hist(data_respon, breaks = 30, freq = FALSE, col = "lightgreen",
     main = "Histogram dan PDF Teoretis Eksponensial",
     xlab = "Waktu Respon (detik)")
curve(dexp(x, rate = rate), add = TRUE, col = "red", lwd = 2)

# 7) Uji Kesesuaian Distribusi Eksponensial
# a) Kolmogorov–Smirnov Test
ks_test <- ks.test(data_respon, "pexp", rate = rate)
ks_test
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  data_respon
## D = 0.059573, p-value = 0.02828
## alternative hypothesis: two-sided
# b) Chi-Square Test (binned)
# Membuat interval (bin)
breaks <- seq(0, max(data_respon), length.out = 10)

# Frekuensi teramati
observed <- hist(data_respon, breaks = breaks, plot = FALSE)$counts

# Probabilitas teoretis antar bin
theoretical_probs <- diff(pexp(breaks, rate = rate))

# Pastikan jumlah probabilitas = 1
theoretical_probs <- theoretical_probs / sum(theoretical_probs)

# Jalankan uji Chi-square
chisq_test <- chisq.test(x = observed, p = theoretical_probs)
## Warning in chisq.test(x = observed, p = theoretical_probs): Chi-squared
## approximation may be incorrect
chisq_test
## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 18.017, df = 8, p-value = 0.0211

3. Gamma

Jumlah kesalahan pada batch produksi
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010

n <- 800
shape <- 3.5
scale <- 2
data_batch <- rgamma(n, shape = shape, scale = scale)

Tentukan:
1) Densitas pada x = 6
2) CDF pada q = 6
3) Kuantil pada p = 0.975
4) Probabilitas antara 2 dan 10 kesalahan
5) Statistik deskriptif
6) Plot density & histogram + overlay teoritis gamma
7) Uji kesesuaian distribusi gamma

set.seed(013)

n <- 800
shape <- 3.5
scale <- 2

data_batch <- rgamma(n, shape = shape, scale = scale)

# 1) Densitas pada x = 6
densitas_x6 <- dgamma(6, shape = shape, scale = scale)
densitas_x6
## [1] 0.1167652
# 2) CDF pada q = 6
cdf_q6 <- pgamma(6, shape = shape, scale = scale)
cdf_q6
## [1] 0.4602506
# 3) Kuantil pada p = 0.975
kuantil_975 <- qgamma(0.975, shape = shape, scale = scale)
kuantil_975
## [1] 16.01276
# 4) Probabilitas antara 2 dan 10 kesalahan
prob_2_10 <- pgamma(10, shape = shape, scale = scale) - pgamma(2, shape = shape, scale = scale)
prob_2_10
## [1] 0.7712669
# 5) Statistik deskriptif
summary(data_batch)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.5486  4.3212  6.4195  7.0558  9.1219 21.4524
sd(data_batch)
## [1] 3.662554
# 6) Plot density & histogram + overlay teoritis Gamma
hist(data_batch, breaks = 30, freq = FALSE, 
     main = "Histogram & Kurva Teoritis Gamma",
     xlab = "Jumlah Kesalahan", col = "skyblue", border = "white")
curve(dgamma(x, shape = shape, scale = scale), 
      col = "red", lwd = 2, add = TRUE)

# 7) Uji kesesuaian distribusi Gamma (Chi-Square)
breaks <- seq(0, max(data_batch), length.out = 10)
observed <- hist(data_batch, breaks = breaks, plot = FALSE)$counts
theoretical_probs <- diff(pgamma(breaks, shape = shape, scale = scale))
theoretical_probs <- theoretical_probs / sum(theoretical_probs)
chisq_test <- chisq.test(x = observed, p = theoretical_probs)
## Warning in chisq.test(x = observed, p = theoretical_probs): Chi-squared
## approximation may be incorrect
chisq_test
## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 2.526, df = 8, p-value = 0.9605

4. chi-square

Statistik χ² dari Simulasi (df berbeda)
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010

n <- 500
df <- 4
data_chi <- rchisq(n, df = df)

Tentukan:
1) Densitas pada x = 7
2) CDF pada q = 7
3) Kuantil pada p = 0.90
4) Probabilitas antara 1.5 dan 6
5) Statistik deskriptif
6) Plot density & histogram (bandingkan dengan teoritis χ²(df=4))
7) Uji kesesuaian χ²

set.seed(013)
n <- 500
df <- 4
data_chi <- rchisq(n, df = df)

# 1) Densitas pada x = 7
densitas_x7 <- dchisq(7, df = df)
densitas_x7
## [1] 0.05284542
# 2) CDF pada q = 7
cdf_q7 <- pchisq(7, df = df)
cdf_q7
## [1] 0.8641118
# 3) Kuantil pada p = 0.90
kuantil_90 <- qchisq(0.90, df = df)
kuantil_90
## [1] 7.77944
# 4) Probabilitas antara 1.5 dan 6
prob_1_5_6 <- pchisq(6, df = df) - pchisq(1.5, df = df)
prob_1_5_6
## [1] 0.6274932
# 5) Statistik deskriptif
summary(data_chi)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2024  2.0459  3.6309  4.2423  5.7102 15.4055
sd(data_chi)
## [1] 2.894519
# 6) Plot density & histogram + overlay teoritis X^2(df=4)
hist(data_chi, breaks = 30, freq = FALSE,
     main = "Histogram & Kurva Teoritis Chi-Square (df=4)",
     xlab = "Nilai X²", col = "lightblue", border = "white")
curve(dchisq(x, df = df), col = "red", lwd = 2, add = TRUE)

# 7) Uji kesesuaian distribusi Chi-Square (Chi-Square Goodness of Fit)
breaks <- seq(0, max(data_chi), length.out = 10)
observed <- hist(data_chi, breaks = breaks, plot = FALSE)$counts
theoretical_probs <- diff(pchisq(breaks, df = df))
theoretical_probs <- theoretical_probs / sum(theoretical_probs)
chisq_test <- chisq.test(x = observed, p = theoretical_probs)
## Warning in chisq.test(x = observed, p = theoretical_probs): Chi-squared
## approximation may be incorrect
chisq_test
## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 19.458, df = 8, p-value = 0.01259

5. Normal

Waktu belajar mahasiswa per minggu (jam)
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010

n <- 1200
mu <- 12
sigma <- 3
data_belajar <- rnorm(n, mean = mu, sd = sigma)

Tentukan:
1) Densitas pada x = 10
2) CDF pada q = 10
3) Kuantil pada p = 0.975
4) Probabilitas antara 8 dan 15 jam
5) Statistik deskriptif + uji normalitas (Shapiro/Wilcox untuk sampel atau KS)
6) Plot density & histogram + theoretical normal curve
7) Uji kesesuaian distribusi normal

set.seed(013)

n <- 1200
mu <- 12
sigma <- 3
data_belajar <- rnorm(n, mean = mu, sd = sigma)

# 1) Densitas pada x = 10
densitas_x10 <- dnorm(10, mean = mu, sd = sigma)
densitas_x10
## [1] 0.1064827
# 2) CDF pada q = 10
cdf_q10 <- pnorm(10, mean = mu, sd = sigma)
cdf_q10
## [1] 0.2524925
# 3) Kuantil pada p = 0.975
kuantil_975 <- qnorm(0.975, mean = mu, sd = sigma)
kuantil_975
## [1] 17.87989
# 4) Probabilitas antara 8 dan 15 jam
prob_8_15 <- pnorm(15, mean = mu, sd = sigma) - pnorm(8, mean = mu, sd = sigma)
prob_8_15
## [1] 0.7501335
# 5) Statistik deskriptif + uji normalitas
summary(data_belajar)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.466   9.979  11.962  12.025  14.064  22.767
sd(data_belajar)
## [1] 3.047814
# Uji normalitas Shapiro-Wilk (untuk sampel kecil < 5000)
shapiro.test(data_belajar[1:5000])
## 
##  Shapiro-Wilk normality test
## 
## data:  data_belajar[1:5000]
## W = 0.99777, p-value = 0.1022
# Uji Kolmogorov–Smirnov (untuk uji kesesuaian terhadap distribusi normal teoritis)
ks.test(data_belajar, "pnorm", mean = mu, sd = sigma)
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  data_belajar
## D = 0.019543, p-value = 0.7491
## alternative hypothesis: two-sided
# 6) Plot density & histogram + theoretical normal curve
hist(data_belajar, breaks = 30, freq = FALSE,
     main = "Histogram & Kurva Teoritis Normal (μ=12, σ=3)",
     xlab = "Jam Belajar", col = "lightblue", border = "white")
curve(dnorm(x, mean = mu, sd = sigma), col = "red", lwd = 2, add = TRUE)

# 7) Uji kesesuaian distribusi normal (Chi-Square Goodness of Fit)
breaks <- seq(min(data_belajar), max(data_belajar), length.out = 12)
observed <- hist(data_belajar, breaks = breaks, plot = FALSE)$counts
expected_probs <- diff(pnorm(breaks, mean = mu, sd = sigma))
expected_probs <- expected_probs / sum(expected_probs)
chisq_test <- chisq.test(x = observed, p = expected_probs)
## Warning in chisq.test(x = observed, p = expected_probs): Chi-squared
## approximation may be incorrect
chisq_test
## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 17.366, df = 10, p-value = 0.06664

6. F Distribution

Latihan Perbandingan Tinggi Badan Atlet Basket
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010

n1 <- 40 # Ukuran sampel grup 1 (junior)
n2 <- 50 # Ukuran sampel grup 2 (senior)
df1 <- n1 - 1 # Derajat kebebasan grup 1
df2 <- n2 - 1 # Derajat kebebasan grup 2

Data tinggi badan dalam cm

data_grup1 <- rnorm(n1, mean = 175, sd = 8) # Junior rata-rata 175 cm
data_grup2 <- rnorm(n2, mean = 185, sd = 7) # Senior rata-rata 185 cm

Tentukan :
1) Densitas pada nilai F yang dihitung
2) CDF untuk nilai F yang dihitung
3) Quantile pada p = 0.95
4) Menghitung Probabilitas nilai F kurang dari 5
5) Menghitung Statistik Deskriptif
6) Plot densitas
7) Uji Kesesuaian Distribusi F

set.seed(013)

# Ukuran sampel
n1 <- 40   # grup 1 (junior)
n2 <- 50   # grup 2 (senior)

# Derajat kebebasan
df1 <- n1 - 1
df2 <- n2 - 1

# Data tinggi badan (cm)
data_grup1 <- rnorm(n1, mean = 175, sd = 8)  
data_grup2 <- rnorm(n2, mean = 185, sd = 7) 

# Varians masing-masing grup
var1 <- var(data_grup1)
var2 <- var(data_grup2)

# Nilai F yang dihitung
F_hitung <- var1 / var2
F_hitung
## [1] 1.136653
# 1) Densitas pada nilai F yang dihitung
densitas_F <- df(F_hitung, df1 = df1, df2 = df2)
densitas_F
## [1] 1.05148
# 2) CDF untuk nilai F yang dihitung
cdf_F <- pf(F_hitung, df1 = df1, df2 = df2)
cdf_F
## [1] 0.6671558
# 3) Kuantil pada p = 0.95
kuantil_95 <- qf(0.95, df1 = df1, df2 = df2)
kuantil_95
## [1] 1.642751
# 4) Probabilitas nilai F kurang dari 5
prob_F_kurang5 <- pf(5, df1 = df1, df2 = df2)
prob_F_kurang5
## [1] 0.9999999
# 5) Statistik deskriptif
summary_F <- c(mean = mean(c(data_grup1, data_grup2)),
               var1 = var1,
               var2 = var2,
               F_value = F_hitung)
summary_F
##       mean       var1       var2    F_value 
## 180.396248  54.745837  48.164075   1.136653
# 6) Plot densitas F teoritis
x <- seq(0, 5, length = 200)
plot(x, df(x, df1 = df1, df2 = df2), type = "l", lwd = 2, col = "blue",
     main = "Kurva Distribusi F",
     xlab = "Nilai F", ylab = "Densitas")
abline(v = F_hitung, col = "red", lwd = 2, lty = 2)
legend("topright", legend = c("Densitas F Teoritis", "F Hitung"),
       col = c("blue", "red"), lty = c(1, 2), lwd = 2)

# 7) Uji kesesuaian distribusi F (Kolmogorov–Smirnov)
# Simulasikan data acak F sesuai df1 & df2
data_Fsim <- rf(1000, df1 = df1, df2 = df2)
ks.test(data_Fsim, "pf", df1 = df1, df2 = df2)
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  data_Fsim
## D = 0.018683, p-value = 0.8762
## alternative hypothesis: two-sided

7. T Distribution

Nilai ujian Komputasi Statistika
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010

n <- 900
df <- 8
data_t <- rt(n, df = df) * 6 + 75 # transformasi ke skala skor

Tentukan:
1) Densitas pada x = 80
2) CDF pada q = 80
3) Kuantil pada p = 0.95
4) Probabilitas antara 70 dan 85
5) Statistik deskriptif
6) Plot density & histogram (bandingkan dengan t-theoretical pada transformasi yang sesuai)
7) Uji kesesuaian ke distribusi t

set.seed(013)
n <- 900
df <- 8
data_t <- rt(n, df = df) * 6 + 75

# 1) Densitas pada x = 80
x <- 80
densitas <- dt((x - 75) / 6, df = df) / 6 
densitas
## [1] 0.04431375
# 2) CDF pada q = 80
cdf <- pt((80 - 75) / 6, df = df)
cdf
## [1] 0.7855833
# 3) Kuantil pada p = 0.95
kuantil <- qt(0.95, df = df) * 6 + 75
kuantil
## [1] 86.15729
# 4) Probabilitas antara 70 dan 85
prob <- pt((85 - 75) / 6, df = df) - pt((70 - 75) / 6, df = df)
prob
## [1] 0.7185129
# 5) Statistik deskriptif
library(moments)
deskriptif <- c(mean = mean(data_t),
                median = median(data_t),
                sd = sd(data_t),
                skewness = skewness(data_t),
                kurtosis = kurtosis(data_t))
deskriptif
##       mean     median         sd   skewness   kurtosis 
## 75.3384888 75.3568340  6.9654213  0.0101323  3.8750502
# 6) Plot density & histogram (bandingkan dengan t-teoritis)
hist(data_t, probability = TRUE, breaks = 30, col = "lightblue",
     main = "Distribusi Nilai Ujian Komputasi Statistika",
     xlab = "Nilai Ujian", ylab = "Densitas")
lines(density(data_t), col = "red", lwd = 2)
x_seq <- seq(min(data_t), max(data_t), length = 200)
lines(x_seq, dt((x_seq - 75) / 6, df = df) / 6, col = "blue", lwd = 2)
legend("topright", legend = c("Data Empiris", "t Teoritis"),
       col = c("red", "blue"), lwd = 2)

# 7) Uji kesesuaian ke distribusi t
# Transformasi balik ke skala t standar
data_t_std <- (data_t - 75) / 6
ks.test(data_t_std, "pt", df = df)
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  data_t_std
## D = 0.037732, p-value = 0.1541
## alternative hypothesis: two-sided

8. Weibull

Umur Rata-rata Komponen Elektronik (jam)
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010
n <- 1000
shape <- 1.8
scale <- 400
data_komponen <- rweibull(n, shape = shape, scale = scale)

Tentukan:
1) Densitas pada x = 350
2) CDF pada q = 350
3) Kuantil pada p = 0.6
4) Probabilitas antara 200 dan 450 jam
5) Statistik deskriptif
6) Plot density & histogram + overlay weibull teoritis
7) Uji kesesuaian distribusi Weibull

set.seed(013)
n <- 1000
shape <- 1.8
scale <- 400
data_komponen <- rweibull(n, shape = shape, scale = scale)

# 1) Densitas pada x = 350
x <- 350
densitas <- dweibull(x, shape = shape, scale = scale)
densitas
## [1] 0.001842097
# 2) CDF pada q = 350
cdf <- pweibull(350, shape = shape, scale = scale)
cdf
## [1] 0.5444945
# 3) Kuantil pada p = 0.6
kuantil <- qweibull(0.6, shape = shape, scale = scale)
kuantil
## [1] 381.0372
# 4) Probabilitas antara 200 dan 450 jam
prob <- pweibull(450, shape = shape, scale = scale) - pweibull(200, shape = shape, scale = scale)
prob
## [1] 0.459883
# 5) Statistik deskriptif
library(moments)
deskriptif <- c(mean = mean(data_komponen),
                median = median(data_komponen),
                sd = sd(data_komponen),
                skewness = skewness(data_komponen),
                kurtosis = kurtosis(data_komponen))
deskriptif
##        mean      median          sd    skewness    kurtosis 
## 359.6231717 318.2397745 215.2994329   0.8267115   3.4515825
# 6) Plot density & histogram (overlay Weibull teoritis)
hist(data_komponen, probability = TRUE, breaks = 30, col = "lightblue",
     main = "Distribusi Umur Komponen Elektronik (Weibull)",
     xlab = "Umur Komponen (jam)", ylab = "Densitas")
lines(density(data_komponen), col = "red", lwd = 2)
x_seq <- seq(min(data_komponen), max(data_komponen), length = 200)
lines(x_seq, dweibull(x_seq, shape = shape, scale = scale), col = "blue", lwd = 2)
legend("topright", legend = c("Data Empiris", "Weibull Teoritis"),
       col = c("red", "blue"), lwd = 2)

# 7) Uji kesesuaian distribusi Weibull
ks.test(data_komponen, "pweibull", shape = shape, scale = scale)
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  data_komponen
## D = 0.031545, p-value = 0.2727
## alternative hypothesis: two-sided

9. Beta Distribution

Proporsi Sukses Kampanye (0–1)
set.seed(010) #gunakan 3 digit terakhir nim ex 3338240010
n <- 800
alpha <- 3
beta <- 4
data_prop <- rbeta(n, shape1 = alpha, shape2 = beta)

Tentukan:
1) Densitas pada x = 0.4
2) CDF pada q = 0.4
3) Kuantil pada p = 0.90
4) Probabilitas antara 0.25 dan 0.6
5) Statistik deskriptif
6) Plot density & histogram + overlay beta teoritis
7) Uji kesesuaian distribusi Beta

set.seed(013)
n <- 800
alpha <- 3
beta <- 4
data_prop <- rbeta(n, shape1 = alpha, shape2 = beta)

# 1) Densitas pada x = 0.4
densitas_x <- dbeta(0.4, alpha, beta)
densitas_x
## [1] 2.0736
# 2) CDF pada q = 0.4
cdf_q <- pbeta(0.4, alpha, beta)
cdf_q
## [1] 0.45568
# 3) Kuantil pada p = 0.90
kuantil_p <- qbeta(0.90, alpha, beta)
kuantil_p
## [1] 0.6668056
# 4) Probabilitas antara 0.25 dan 0.6
prob_interval <- pbeta(0.6, alpha, beta) - pbeta(0.25, alpha, beta)
prob_interval
## [1] 0.6513664
# 5) Statistik deskriptif
summary(data_prop)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.02661 0.29364 0.42165 0.42631 0.55248 0.91529
mean(data_prop)
## [1] 0.4263074
var(data_prop)
## [1] 0.03134557
sd(data_prop)
## [1] 0.1770468
# 6) Plot density & histogram dengan overlay Beta teoritis
hist(data_prop, probability = TRUE, col = "skyblue", border = "white",
     main = "Histogram & Density - Distribusi Beta(3,4)",
     xlab = "Proporsi Sukses Kampanye")
curve(dbeta(x, alpha, beta), add = TRUE, col = "red", lwd = 2)
lines(density(data_prop), col = "darkblue", lwd = 2, lty = 2)
legend("topright", legend = c("Teoritis Beta", "Kernel Density"),
       col = c("red", "darkblue"), lty = c(1, 2), lwd = 2)

# 7) Uji kesesuaian distribusi Beta
# Gunakan Kolmogorov-Smirnov test
ks.test(data_prop, "pbeta", alpha, beta)
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  data_prop
## D = 0.024498, p-value = 0.723
## alternative hypothesis: two-sided